Boil 3 eggs 10 to 12 minutes, plunge into cold water; peel.
Press hard-cooked eggs through a fine strainer into a large bowl.
Stir in 1 egg yolk and powdered sugar.
Gradually work in butter and vanilla.
Add flour; knead to make a soft dough.
Press into a ball and wrap in foil or plastic wrap.
Refrigerate 1 hour.
Preheat oven to 375°F (190°C).
Divide dough into small pieces.
Form each piece into a roll about 4 inches (10 cm) long.
Brush ends of rolls with beaten egg yolk; join ends to make rings.
Brush tops generously with beaten egg yolk; sprinkle with sugar crystals.
Place on baking sheets.
Bake 10 to 12 minutes or until golden.
Remove from baking sheets with a spatula; cool on a rack.